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Results tagged with gr.group-theory
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user 2284
Questions about the branch of algebra that deals with groups.
11
votes
Accepted
Class field towers
Let $\ell$ be an odd prime and $m$ an integer such that
$$|\{p|m,\ p\equiv1\operatorname{mod} \ell\}|\geq8.$$
Then Y.Furuta proved that $\mathbb Q(\zeta_m)$ admits an infinite unramified $\ell$-class …
- 10.9k
7
votes
Cohomology of $SL_2(\mathbb{F}_p)$ acting on trace zero matrices over $\mathbb{F}_p$
It seems to me that Sah's lemma will do the trick.
(Sah's lemma) Let $G$ be a group, $M$ a $G$-representation and $g\in Z(G)$. Then $x\mapsto (g-1)x$ is the zero map on $H^{1}(G,M)$.
The proof i …
- 10.9k
7
votes
2
answers
440
views
Pre-images of unipotent elements in $\operatorname{SL}_{n}(A)$
The starting point of this question is the (presumably) well-known theorem (the proof I know is from Abelian $\ell$-adic representations and elliptic curves from J-P.Serre in which it is a lemma for $ …
- 10.9k